A Study on the Computation Accuracy of the Aberrational Diffraction Images

Abstract

Some modifications are introduced in the numerical method described previously by Hopkins and Yzuel in order to improve its accuracy. The area elements in which the exit pupil is divided for the integration are equal in the methods proposed here. These methods differ on the radial variable used. The influence of the exact evaluation of the phase function derivatives on the final accuracy with respect to the approximate evaluation by finite differences is studied. The methods developed here are applied to several optical systems with different wave aberration polynomials. We study the minimum number of area elements needed on the integration to obtain the intensity on points of the image plane with a given accuracy. A discussion of the results is described in the graphs and the tables of the second part of this paper.